As the debate over gun rights heats up on Capitol Hill, the Supreme Court on Monday denied a petition to hear a challenge to a key provision of New York state’s restrictive gun laws.

The high court without comment refused to take up a petition challenging a lower court’s upholding New York state’s requirement that citizens prove “proper cause” to carry a weapon for self-defense outside the home.

“Our review of the history and tradition of firearm regulation does not ‘clearly demonstrate’ that limiting handgun possession in public to those who show a special need for self-protection is inconsistent with the Second Amendment,” Judge Richard C. Wesley wrote in the November opinion.

A group of New Yorkers challenging the requirement asked the Supreme Court in January to take up the case.

“Every day, my office fights to ensure all New Yorkers are safe and secure in their communities,” Mr. Schneiderman said in a statement. “This means making sure that our state’s gun safety laws are protected and vigorously enforced. New York State has enacted sensible and effective regulations of concealed handguns, and this decision keeps those laws in place. This is a victory for families across New York who are rightly concerned about the scourge of gun violence that all too often plagues our communities.”

“As the court of appeals held, New York’s proper-cause requirement does not confer unbridled discretion on licensing officials, but rather frames a well-defined and objective inquiry guided by a body of New York judicial decisions,” Mr. Schneiderman wrote in a brief last month. “The court of appeals aptly observed that petitioners are not really complaining because there is no licensing standard under New York law, but rather are complaining because they ‘do not like’ the standard that New York law imposes.”

Alan Gura, counsel for the plaintiffs — five residents who had applied for a “full-carry license” — disagreed.

“The only thing worse than explicitly refusing to enforce an enumerated constitutional right would be to declare a right ‘fundamental’ while standing aside as lower courts render it worthless,” Mr. Gura wrote in a reply brief on March 26. “Few outcomes could promote as much cynicism about our legal system.”

Legal challenges to New York’s strict new gun measures passed in the wake of December’s school shooting rampage, such as bans to assault-style weapons and high-capacity magazines, are still pending.

The question of whether or not carrying a gun for protection outside the home is a constitutional right is also being litigated elsewhere in the country.

A federal court in February denied a petition to rehear a December ruling that declared an Illinois law prohibiting people from carrying concealed handguns in public unconstitutional. The court had given the Illinois legislature 180 days to pass some kind of concealed-carry law.

Illinois Democratic Gov. Pat Quinn has said he wants state Attorney General Lisa Madigan to appeal to the Supreme Court, but Ms. Madigan has indicated she wants to see what the legislature comes up with before making a decision.